Understanding Short-Horizon Bias in Stochastic Meta-Optimization
Bibliographic record
Abstract
Careful tuning of the learning rate, or even schedules thereof, can be crucial to effective neural net training. There has been much recent interest in gradient-based meta-optimization, where one tunes hyperparameters, or even learns an optimizer, in order to minimize the expected loss when the training procedure is unrolled. But because the training procedure must be unrolled thousands of times, the meta-objective must be defined with an orders-of-magnitude shorter time horizon than is typical for neural net training. We show that such short-horizon meta-objectives cause a serious bias towards small step sizes, an effect we term short-horizon bias. We introduce a toy problem, a noisy quadratic cost function, on which we analyze short-horizon bias by deriving and comparing the optimal schedules for short and long time horizons. We then run meta-optimization experiments (both offline and online) on standard benchmark datasets, showing that meta-optimization chooses too small a learning rate by multiple orders of magnitude, even when run with a moderately long time horizon (100 steps) typical of work in the area. We believe short-horizon bias is a fundamental problem that needs to be addressed if meta-optimization is to scale to practical neural net training regimes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".